scholarly journals Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lazim Abdullah ◽  
Noor Azzah Awang ◽  
Mahmod Othman
Keyword(s):  
Shapley Value ◽  
Choquet Integral ◽  
Evaluation Process ◽  
Aggregation Operator ◽  
Interaction Index ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
New Development ◽  
The Future

Choquet integral is a type of aggregation operator that is commonly used to aggregate the interrelated information. Nowadays, this operator has been successfully embedded with fuzzy measures in solving various evaluation problems. Inspired from this new development, this paper aims to introduce a combined Choquet integral-fuzzy measures (CI-FM) operator that uses the Shapley value standard and interaction index to deal with the interactions between elements of information. The proposed operator takes into account not only the importance of elements or their ordered positions but also the interaction among criteria during the evaluation process. A case of customers’ satisfaction over two fast restaurants in Malaysia is presented to illustrate the application of the proposed aggregation operator. Based on three customers’ satisfaction criteria, restaurant 1 and restaurant 2 received CI-FM scores of 0.711011 and 0.704945, respectively. Interestingly, the criterion “services” constantly received the highest rating across both restaurants. In addition, the proposed aggregation operator successfully identified which restaurant is superior in the eyes of customers. Finally, this study offers some research ideas for the future.

SOME RELATIONS AMONG VALUES, INTERACTIONS, AND DECOMPOSABILITY OF NON-ADDITIVE MEASURES

2007 ◽  
Vol 15 (02) ◽  
pp. 175-191 ◽  
Author(s):  
KATSUSHIGE FUJIMOTO ◽  
TOSHIAKI MUROFUSHI
Keyword(s):  
Shapley Value ◽  
Choquet Integral ◽  
Single Element ◽  
Interaction Index ◽  
The Shapley Value ◽  
Additive Measures

We will discuss some relations among values, i.e., global / overall importance of each single element of the object to be considered, interaction indices, i.e., simultaneous interaction among the elements in a coalition, and inclusion-exclusion coverings, i.e., decomposability of non-additive measures and / or of the Choquet integral. So, we show that inclusion-exclusion coverings are characterized by the Shapley interaction index. Then, inclusion-exclusion coverings are invariant under the transformations which characterize the Shapley value and / or the Shapley interaction index, and preserve the Shapley value.

scholarly journals A Novel Algorithm Based on 2-Additive Measure and Shapley Value and Its Application in Land Pollution Remediation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jian Lin ◽  
Qiongling Wu ◽  
Riqing Chen ◽  
Zhiyong Tian
Keyword(s):  
Shapley Value ◽  
Group Decision ◽  
Young Inequality ◽  
Aggregation Operator ◽  
Additive Measure ◽  
Pollution Remediation ◽  
Heterogeneous Information ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
Special Cases

In this article, a new aggregation operator called the Young–Shapley optimal weight (Y-SOW) operator is proposed to aggregate heterogeneous information in group decision-making. The Y-SOW operator combines the Shapley value with the Young inequality. Meanwhile, a series of special cases and main properties of the Y-SOW operator are studied. Furthermore, the dispersion maximization model of the Y-SOW operator is established to obtain the optimal 2-additive measure. In the Shapley value method of the cooperative game, the 2-additive measure not only simplifies the complexity of fuzzy measures but also solves the interaction between attributes. The Shapley value of the 2-additive measure is explored to the weight of the Y-SOW operator. Finally, the Y-SOW operator-based multiattribute group decision (YSMGAD) algorithm is proposed. The application of the YSMGAD algorithm for land pollution remediation is analyzed.

scholarly journals CAPACITIES AND GAMES ON LATTICES: A SURVEY OF RESULTS

2006 ◽  
Vol 14 (04) ◽  
pp. 371-392 ◽  
Author(s):  
MICHEL GRABISCH
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Characteristic Form ◽  
Möbius Transform ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
Power Set ◽  
Recent Developments

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

scholarly journals Research on Profit Distribution of Software Outsourcing Alliances Based on the Improved Shapley Value Model

2013 ◽  
Vol 13 (Special-Issue) ◽  
pp. 100-109
Author(s):  
Xiyan Lv ◽  
Suyan Zhao
Keyword(s):  
Shapley Value ◽  
Influence Factors ◽  
Distribution Method ◽  
Software Outsourcing ◽  
Profit Distribution ◽  
Theoretical Support ◽  
The Shapley Value ◽  
The Future ◽  
Value Model

Abstract With the development of software outsourcing industry, there is a growing trend to establish the software outsourcing alliances. Whether alliances’ profit distribution is reasonable affects directly and significantly alliances’ stability. This paper introduces the Shapley value method which is a common profit distribution method applicable to multiple people cooperation. Due to the weakness of the Shapley value method, AHP is used to analyze the influence factors and adjust the model. The anticipated outcome of the result is to provide a theoretical support for the profit distribution of the software outsourcing alliances in the future.

Regional integrated energy system schemes selection based on risk expectation and Mahalanobis-Taguchi system

2021 ◽  
pp. 1-18
Author(s):  
Jiahang Yuan ◽  
Yun Li ◽  
Xinggang Luo ◽  
Lingfei Li ◽  
Zhongliang Zhang ◽  
...  
Keyword(s):  
Energy Demand ◽  
Choquet Integral ◽  
Subjective Evaluation ◽  
Risk Attitude ◽  
Energy System ◽  
Energy Utilization ◽  
Utilization Efficiency ◽  
Energy Structure ◽  
Fuzzy Measures ◽  
Integrated Energy System

Regional integrated energy system (RIES) provides a platform for coupling utilization of multi-energy and makes various energy demand from client possible. The suitable RIES composition scheme will upgrade energy structure and improve integrated energy utilization efficiency. Based on a RIES construction project in Jiangsu province, this paper proposes a new multi criteria decision-making (MCDM) method for the selection of RIES schemes. Because that subjective evaluation on RIES schemes benefit under criteria has uncertainty and hesitancy, intuitionistic trapezoidal fuzzy number (ITFN) which has the better capability to model ill-known quantities is presented. In consideration of risk attitude and interdependency of criteria, a new decision model with risk coefficients, Mahalanobis-Taguchi system and Choquet integral is proposed. Firstly, the decision matrices given by experts are normalized, and then are transformed to minimum expectation matrices according to different risk coefficients. Secondly, the weights of criteria from different experts are calculated by Mahalanobis-Taguchi system. Mobius transformation coefficients based on interaction degree are to calculate 2-order additive fuzzy measures, and then the comprehensive weights of criteria are obtained by fuzzy measures and Choquet integral. Thirdly, based on group decision consensus requirement, the weights of experts are obtained by the maximum entropy and grey correlation. Fourthly, the minimum expectation matrices are aggregated by the intuitionistic trapezoidal fuzzy Bonferroni mean operator. Thus, the ranking result according to the comparison rules using the minimum expectation and the maximum expectation is obtained. Finally, an illustrative example is taken in the present study to make the proposed method comprehensible.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

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